Degrees of Freedom

PROC SURVEYFREQ uses the degrees of freedom of the variance estimator to obtain the t-percentile for confidence limits for proportions, totals, and other statistics. The procedure also uses the degrees of freedom in computing the F statistics for the Rao-Scott and Wald chi-square tests.

PROC SURVEYFREQ computes the degrees of freedom based on the variance estimation method and the sample design. Alternatively, you can specify the degrees of freedom in the DF= option in the TABLES statement instead of having the procedure compute it.

For Taylor series variance estimation, PROC SURVEYFREQ calculates the degrees of freedom (df) as the number of clusters minus the number of strata. If there are no clusters, then df equals the number of observations minus the number of strata. If the design is not stratified, then df equals the number of clusters minus one. These numbers are based on the observations included in the analysis of the individual table request. These numbers do not count observations that are excluded from the table due to missing values. See the section Missing Values for details. If you specify the MISSING option, missing values are treated as valid nonmissing levels and are included in computing degrees of freedom. If you specify the NOMCAR option for Taylor series variance estimation, observations with missing values of the TABLES variables are included in computing degrees of freedom.

If you provide replicate weights with a REPWEIGHTS statement, the degrees of freedom is equal the number of replicates, which is the number of REPWEIGHTS variables that you provide. Alternatively, you can specify the degrees of freedom in the DF= option in the REPWEIGHTS or TABLES statement.

For BRR variance estimation (when you do not use a REPWEIGHTS statement), PROC SURVEYFREQ calculates the degrees of freedom as the number of strata. PROC SURVEYFREQ bases the number of strata on all valid observations in the data set, unless you specify the DFADJ method-option for VARMETHOD=BRR. When you specify the DFADJ option, the procedure computes the degrees of freedom as the number of nonmissing strata for the individual table request. This excludes any empty strata that occur when observations with missing values of the TABLES variables are removed from the analysis for that table.

For jackknife variance estimation (when you do not use a REPWEIGHTS statement), PROC SURVEYFREQ calculates the degrees of freedom as the number of clusters minus the number of strata. If there are no clusters, then df equals the number of observations minus the number of strata. If the design is not stratified, then df equals the number of clusters minus one. For jackknife variance estimation, PROC SURVEYFREQ bases the number of strata and clusters on all valid observations in the data set, unless you specify the DFADJ method-option for VARMETHOD=JACKKNIFE. When you specify the DFADJ option, the procedure computes the degrees of freedom from the number of nonmissing strata and clusters for the individual table request. This excludes any empty strata or clusters that occur when observations with missing values of the TABLES variables are removed from the analysis for that table.

For each table request, PROC SURVEYFREQ produces a nondisplayed ODS table, "Table Summary," which contains the number of (nonmissing) observations, strata, and clusters that are included in the analysis of the table. If there are missing observations, empty strata, or empty clusters excluded from the analysis, the "Table Summary" data set also contains this information. If you request confidence limits or chi-square tests, which depend on the degrees of freedom of the variance estimator, the "Table Summary" data set provides the degrees of freedom df. See Example 84.3 for more information about this output data set.